Creating high-quality is expensive as it requires significant manual input to generate diverse yet plausible geometric and topological variations, with and without textures. Hence, there is a strong demand for generative models producing novel, diverse, and realistic 3D shapes along with associated part semantics and structure. A key challenge towards this goal is how to accommodate diverse shape, including both continuous deformations of parts as well as structural or discrete alterations which add to, remove from, or modify the shape constituents and compositional structure. In this talk I will present StructureNet, a hierarchical graph network which can directly encode shapes represented as such n-ary graphs; can be robustly trained on large and complex shape families; and be used to generate a great diversity of realistic structured shape geometries. The learned latent spaces enable several structure-aware geometry processing applications, including shape generation and interpolation, shape editing, or shape structure discovery directly from un-annotated images, point clouds, or partial scans.